Question

Разложить на множители: 22. 3x+cy+cx+3y. 23. 5a-5b+ap-bp. 24. ab+ac-b-c. 25 x5-3x3+4x2-12. 26. 20a3bc-28ac2+15a2b2-21bc. 27. ax2+ay-bx2-by+cx2+cy. 28.x3-x2+x2y+x-xy+y
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Answer 1

22.

$3x+cy+cx+3y=(3x+3y)+(cx+cy)=3(x+y)+c(x+y)=(x+y)(c+3)$

23.

$5a-5b+ap-bp=(5a-5b)+(ap-bp)=5(a-b)+p(a-b)=(a-b)(5+p)$

24.

$ab+ac-b-c=(ab+ac)-(b+c)=a(b+c)-(b+c)=(b+c)(a-1)$

25.

 $x^5-3x^3+4x^2-12=(x^5-3x^3)+(4x^2-12)=$

$=x^3(x^2-3)+4*(x^2-3)=(x^2-3)*(x^3+4)$

26.

$20a^3bc-28ac^2+15a^2b^2-21bc=(20a^3bc-28ac^2)+(15a^2b^2-21bc)=$

$=4ac*(5a^2b-7c)+3b*(5a^2b-7c)=(5a^2b-7c)*(4ac+3b)$

27.

 $ax^2+ay-bx^2-by+cx^2+cy=(ax^2+ay)-(bx^2+by)+(cx^2+cy)=$

$=a(x^2+y)-b(x^2+y)+c(x^2+y)=(x^2+y)*(a-b+c)$

28.

$x^3-x^2+x^2y+x-xy+y=(x^3-x^2+x)+(x^2y-xy+y)=$

$=x*(x^2-x+1)+y*(x^2-x+1)=(x^2-x+1)*(x+y)$